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Block #261,008

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/15/2013, 3:08:30 AM Β· Difficulty 9.9746 Β· 6,539,474 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
422f4652d5661cb5483d51b3d2602d7feb67e4ce3ebd97ebe907ce02d054c70e
View on Chainz β†—

Height

#261,008

Difficulty

9.974564

Transactions

2

Size

984 B

Version

2

Bits

09f97d06

Nonce

74,560

Timestamp

11/15/2013, 3:08:30 AM

Confirmations

6,539,474

Merkle Root

dc2de33887b9229d3c30011b99fe33ee4b24086299f9a654b8f9d5c515af1e2d
Transactions (2)
Coinbase027c496d3d20fa…50f08b7344bcf6
1 in β†’ 1 out10.0505 XPM109 B
AcfXAki4…76jq4Bqe
2a3fa4191e3cbf…590b22941f59b2
5 in β†’ 1 out11.2160 XPM785 B
ATsGimmm…XWTWknF1
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.694 Γ— 10⁹³(94-digit number)
46944612485636237254…00813010826022434540
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
4.694 Γ— 10⁹³(94-digit number)
46944612485636237254…00813010826022434541
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.388 Γ— 10⁹³(94-digit number)
93889224971272474509…01626021652044869081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.877 Γ— 10⁹⁴(95-digit number)
18777844994254494901…03252043304089738161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.755 Γ— 10⁹⁴(95-digit number)
37555689988508989803…06504086608179476321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.511 Γ— 10⁹⁴(95-digit number)
75111379977017979607…13008173216358952641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.502 Γ— 10⁹⁡(96-digit number)
15022275995403595921…26016346432717905281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.004 Γ— 10⁹⁡(96-digit number)
30044551990807191843…52032692865435810561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.008 Γ— 10⁹⁡(96-digit number)
60089103981614383686…04065385730871621121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.201 Γ— 10⁹⁢(97-digit number)
12017820796322876737…08130771461743242241
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 261008

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 422f4652d5661cb5483d51b3d2602d7feb67e4ce3ebd97ebe907ce02d054c70e

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #261,008 on Chainz β†—
Circulating Supply:57,647,918 XPMΒ·at block #6,800,481 Β· updates every 60s
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